You can of course enter into an arrangement with a company, do work for the company, receive "bitcoins" from the company, and both go on your merry way. But the company "paying" you has exposed itself to extreme liability with the IRS; it is probably on the hook not only for the employers half of dollar-denominated self-employment tax, but for the employee's half as well, plus penalties, interest, and legal fees.
(Might you be conflating payment in bitcoins with payment off the books?)
* There is a dollar-denominated minimum wage
* There is dollar-denominated payroll tax and, for contractors, dollar-denominated self-employment tax that scales in dollar-denominated amounts whether you're paid in moon cakes or rare freshwater fish.
* And, if you're a company principal of a non-passthrough entity, there is an IRS requirement that you be paid a wage that corresponds to the fair market value of your role, and anything you do to not pay yourself a reasonable-looking dollar-denominated wage stands a good chance of getting you audited (this rule being one of the primary ways business owners attempt to avoid paying taxes).
It's only been fairly recently that the Department of Labor has issued opinions about foreign nationals being paid in foreign currency based on the current exchange rate available in the vicinity of the employer; that is, there are very specific cases in which you can pay someone both Euros and Dollars. Making geeky assumptions that, because some PHP program somewhere generates some number people call an "exchange rate" that means Bitcoins get you around the FLSA minimum wage... dubious and risky.
To make it less about me also: How instead would you say to your employer (just accept this as part of the hypothetical question, you work for someone in a fundamentally permanent salaried employ), this is how I want my salary in bitcoins to be set. Or if you are completely incapable of imagining working for someone else, how would you frame a salaried employment for an employee in bitcoins?
Alternatively, the contract could specify that payments will be made in BTC, but the payment amount will depend on an exchange rate with some other instrument such as USD or EUR. In that case the customer is merely providing the exchange function as part of the contract.
A PayPal alternative for BitCoin (think CoinPal), will be a good start for non-geeks. However, the currency needs to have some stability so that people can trust it for their real money.
That seems obvious, so I'm sure I must have mis-understood, or not understood, your question.
In the UK I believe it's possible to agree a salary/payment at an amount of recognized currency, such as GBP or USD, and then you perform all your tax and related calculations based on that. How the payment is actually transferred is, potentially, up to the people involved.
I believe that I can contract my services at, say, 100 GBP per hour, bill for one hour, and then accept payment in bitcoin, stating that there is an agreed rate of exchange. If the stated underlying rates are not regarded as "unusual" by the HMRC then most likely the arrangement would be permitted to stand.
There are laws concerning "payment in kind" and I think this would fall under that. Note, I'm not an accountant or lawyer, but I've seen barter arrangements not dissimilar to this accepted as valid by HMRC.
FLSA 3(m), also read the section in the FLSA handbook about "scrip" and "tokens" (which I understand bitcoin isn't --- scrip, which cannot lawfully be used as a wage substitute, only as an accounting mechanism for dollar-denominated wages) is at least backed by the full faith and credit of a company.